Warped product and quasi-Einstein metrics

Warped products provide a rich class of physically signi cant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a bre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and noncompact complete base manifolds which do not admit any non-trivial Ricci- at quasi-Einstein warped product.